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Published February 2011 | public
Journal Article

On solvable subgroups on automorphism groups of right-angled Artin groups

Abstract

For any right-angled Artin group, we show that its outer automorphism group contains either a finite-index nilpotent subgroup or a nonabelian free subgroup. This is a weak Tits alternative theorem. We find a criterion on the defining graph that determines which case holds. We also consider some examples of solvable subgroups, including one that is not virtually nilpotent and is embedded in a non-obvious way.

Additional Information

© 2011 World Scientific Publishing Company. Received 30 November 2009. Revised 25 February 2010. Communicated by S. Hermiller. I would like to thank the organizers of the 2009 International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory, where I started considering the problem in this paper. I am grateful to Ruth Charney for commenting on an earlier version of this paper. I would also like to thank the anonymous referee for some helpful comments. This research was done under the support of an NSF Mathematical Sciences Postdoctoral Research Fellowship.

Additional details

Created:
August 22, 2023
Modified:
October 23, 2023